Waveguides · Electromagnetics · GATE ECE
Marks 1

Marks 2
A waveguide consists of two infinite parallel plates (perfect conductors) at a separation of 10$$-$$4 cm, with air as the dielectric. Assume the speed of light in air to be 3 $$\times$$ 108 m/s. The frequency/frequencies of TM waves which can propagate in this waveguide is/are ___________.
The cross-sectional dimemsions of the waveguide are given as a = 0.08 m and b = 0.033 m. The mode of propagation inside the waveguide is
$$\cos \,\,(6.283\,\, \times \,\,{10^{10}}t\, - \beta \,z)$$
The phase velocity $${V_p}$$ of the wave inside the waveguide satisfies

where $${H_0}$$ is a constant, a and b are the dimensions along the x-axis and the y-axis respectively. The mode of propagation in the waveguide is

For a wave propagating in an air filled rectangular wave guide
Marks 5
Where $$k = \,\,\eta \,\omega \,\, \in $$
(a) Determine the surface charge densities $${\rho _s}$$ on the plates at x = 0 and x = d
(b) Determine the surface current densities $$\mathop {{J_s}}\limits^ \to $$ on the same plates.
(c) Prove that $${\rho _s}$$ and $$\mathop {{J_s}}\limits^ \to $$ satisfy the current continuity condition.

Where $$k = \,\,\eta \,\omega \,\, \in $$
(a) Determine the surface charge densities $${\rho _s}$$ on the plates at x = 0 and x = d
(b) Determine the surface current densities $$\mathop {{J_s}}\limits^ \to $$ on the same plates.
(c) Prove that $${\rho _s}$$ and $$\mathop {{J_s}}\limits^ \to $$ satisfy the current continuity condition.

Where $$k = \,\,\eta \,\omega \,\, \in $$
(a) Determine the surface charge densities $${\rho _s}$$ on the plates at x = 0 and x = d
(b) Determine the surface current densities $$\mathop {{J_s}}\limits^ \to $$ on the same plates.
(c) Prove that $${\rho _s}$$ and $$\mathop {{J_s}}\limits^ \to $$ satisfy the current continuity condition.

(a) Calculate the cut-off wavelength and the guide wavelength for this mode.
(b) What are the other (TE or TM) modes that can propagate through the waveguide?
(c) If a = b = 2.29 cm, what are the modes which can propagate through the waveguide?

Find the vector magnetic field and the phase velocity of the wave inside the waveguide.
Marks 8
(i) Determine the cutoff frequency of the$$T{E_{11}}$$ mode.
(ii) Determine the frequency at which this / mode has an attenuation of $$3\,\pi $$ nepers/m.
(i) Determine the cutoff frequency of the$$T{E_{11}}$$ mode.
(ii) Determine the frequency at which this / mode has an attenuation of $$3\,\pi $$ nepers/m.